In an effort to standardize the interface of electronic equipment, in certain cases, the industry has established pin assignments for the connectors utilized in the interface. An example is a 68 pin connector utilized for interconnecting to memory cards in various computer applications. This connector has 60 signal pins, 4 ground return pins, and 4 DC voltage pins, all of which are preassigned by the industry. The signal to ground ratio of an electrical connector is equal to the number of signal carrying pins divided by the number of ground return pins in the connector. Since the DC voltage pins, for purposes of the present disclosure, can be considered similar in effect to the AC voltage ground pins, the signal to ground ratio of this 68 pin connector is 7.5 to 1.0. In computer applications, typically, multiple lines are simultaneously switched and all return current generated by this switching must be returned through one of the ground pins. Therefore, the return current of 8 or so signal pins must be accommodated by a single ground pin. This is no problem when the signal rise time is relatively slow, in the 8 to 10 nanosecond range. However, when the rise time is increased, as in certain computer applications, the induced voltage is increased resulting in "ground bounce" or common mode noise in the ground return pins. When ground bounce reaches a high enough level, relative to the level of the signals, the systems may become unable to reliably read and respond to the signals thereby causing what is known in the industry as "false triggering". Since the pin assignments have been fixed by the industry, the signal to ground ratio cannot be altered. However, to reduce the adverse effects of the faster rise times, a conductive shroud may be utilized that electrically interconnects the ground of the memory card to the ground of the equipment with which the card is being used. Such a shroud and related connector are disclosed in U.S. Pat. No. 5,288,247 which issued Feb. 22, 1994 to Kaufman and which is incorporated herein by reference. The shroud of the '247 patent is arranged to enclose the top of the connector and the two sides thereof. Several contacts extend from the shroud and electrically engage a conductive outer surface on a memory card that is mated with the connector. The shroud is electrically connected to ground circuitry on the circuit board and results in greatly improved performance of the equipment. In some equipment it is desirable to utilize more than one memory card, but the additional memory card connectors require significant circuit board space, which may not be available. Therefore, what is needed is a shroud that will accept multiple connectors in a vertically stacked relationship that benefit from the improved performance of the single connector shroud.